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CHICAGO — By the time they reach eighth grade, according to federal tests, half of all African-American schoolboys have not mastered the most basic math skills that educators consider essential for their grade level.

A new paper being released Monday by the National Bureau of Economic Research suggests a promising approach for helping the most challenged students, who often arrive in high school several years behind their peers.

The study, which was conducted by a team led by Jens Ludwig, the co-director of the University of Chicago Urban Education Lab, provided a program of intense tutoring, in combination with group behavioral counseling, to a group of low-income ninth- and 10th-grade African-American youths with weak math skills, track records of absences or disciplinary problems. Those students learned in an eight-month period the equivalent of what the average American high school student learns in math over three years of school, as measured by standardized test scores, over and above what a similar group of students who did not receive the tutoring or counseling did.